Apologies for the offtopic chatter, but I just noticed this as I was
trying to look for Emacs's Matlab mode to see if I could get some
ideas for Octave mode. It appears that the Mathworks only allows the
BSD license on their servers now, which affects much free software
under other licenses (in particular GPL) that they were hosting.

It's difficult to find exactly what happened and how because they seem
to have spread the word about this relatively secretly by email to
people with code on their servers, but they do have a FAQ:

I don't know about anyone else, but I'm deeply disturbed that
Mathworks is now actively fighting against copyleft.

- Jordi G. H.

This seems to be so they can transition to a more 'cloud-like' model. From the FAQ:

Why is the File Exchange adding licensing?

Licensing
clarifies the rights you have as an author and as a user of the code
available on the File Exchange. Licensing details how the file can be
used and addresses common questions around rights to modification,
distribution, and commercial use.

What happens if I don't do anything? Do I have to put a license on my code?

We
have no plans to remove unlicensed submissions, but they will be
prominently marked as unlicensed. In addition, unlicensed contributions
will not be available for use with any future tools that access the
File Exchange from within MathWorks products.

Well being able to download and use code on the Exchange 'automagically' without worrying about license restrictions is probably a good thing. Of course this also means MathWorks can then ship binaries based on your code without sharing the source. BSD vs. GPL: which is freedomier, flame on!

Judd Storrs sums it up well:Loss of free hosting is unfortunate and someone from the FSF should contact the Mathworks to see if any abandoned GPL-licensed packages can be adopted.

However, I really think the major upside is that *everything* on the Mathworks file-exchange can now be used in GPL-licensed work. Is that not significant? There are no non-free-software licenses allowed. Sure you're ticked off that your favorite flavor of freedom wasn't selected. I'm sure others are ticked off that their protective proprietary licenses are now forbidden. Personally, I think it's a good and pragmatic compromise on the Mathworks part because it keeps the license wars off their servers. Nobody's stopping you from hosting your code anywhere else.